You know who would love “The Imaginarium of Doctor Parnassus”? Terry Gilliam. It’s bizarre and whimsical and often beautiful to look at, and it makes no sense whatsoever. It’s totally something Terry Gilliam would dig!

Wait, what? He directed it? And co-wrote the screenplay? Oh. Well, I guess that explains that.

As for who other than Terry Gilliam might enjoy it, I’m at a loss. It’s famous now primarily for being Heath Ledger’s last film — he died before shooting was complete — but we might want to go back to thinking “The Dark Knight” was Ledger’s final movie. This one is baffling, obtuse, and tiresome, like listening to someone tell you about a dream they had. For two hours.

“Imaginarium” is about mysterious old Dr. Parnassus (Christopher Plummer), who operates a traveling sideshow with the assistance of his daughter, Valentina (Lily Cole), who claims to be only 12 but is clearly much older, and a crew that includes a dwarf (Verne Troyer) and a regular guy named Anton (Andrew Garfield). There is a mirror on the stage of this sideshow, and if you walk through the mirror you are transported into your imagination, or possibly into Dr. Parnassus’ imagination, and it’s really crazy there. People aren’t supposed to be just randomly barging into the mirror, although it happens pretty frequently, folks just leaping onto the stage and jumping in. Dr. Parnassus needs a bouncer.

Anyway, along comes Tony (Ledger), an amnesiac of uncertain origin who might be sketchy and who becomes the sideshow’s barker, bringing in more paying customers than the show had been getting. Before long, Tony goes through the mirror himself, whereupon he is played, in his imagination, by Johnny Depp, then Jude Law, then Colin Farrell. (Going into an imaginary dimension changes your face, you see. And I’ll be honest: In my imagination I look like those guys, too.)

Oh, and Parnassus owes the devil (Tom Waits) something, and has to accumulate five “souls” in two days. Something to do with Parnassus being immortal and being a storyteller in an age when no one wants stories anymore. If this is Gilliam expressing his own frustrations over the many setbacks he’s had over the years — and they have been numerous — I would gently point out that people DO want stories, and that “Doctor Parnassus” doesn’t have one. It has a sequence of loosely connected events that do not add up to anything.

The imagination sequences are gorgeously imaginative, however. Production designer Anastasia Masaro and cinematographer Nicola Pecorini deserve praise for bringing Gilliam’s wild fantasies to life — and indeed, this is what Gilliam has always been great at, going back to the surreal animations he did for “Monty Python’s Flying Circus.” But the film’s a mess otherwise, with an incoherent story and no relatable characters, and I’m still left wondering whether anyone outside of Gilliam’s brain will appreciate it.